October 14, 2011Ms. Wu says … find your new seat!

1. Copy homework into planner.2. Get your HW 1.15 out.3. Work on the warm up in pen.4. Grade HW 1.15 (key is on table).________________________________________________

Once you’re done with the warm up, place it in the manila folder.

 

Vocabulary– Compound inequality: an inequality that consists of

two separate inequalities joined by and or or.– Conjunction: a compound inequality with and in which

the graph is the intersection of the graphs of the inequalities

• Find values of the variable for which both inequalities are true

– Disjunction: a compound inequality with or in which the graph is the union of the graphs of the inequalities.

• Find values of the variable for which either one or both of the inequalities are true

• < and > are disjunctions

Relations and Functions

What’s a relation?• {(0,0), (2,1), (4,2)}

• y = 2x• Relation: a set of ordered pairs

• Relation: a set of ordered pairs

What’s a function?Domain Range

• Function: a relation where each value of the domain has exactly one corresponding member of the range

• Each x has one y• Each input has 1 output

Function Mapping

4

Is this a function?

How about now?

Sets of Coordinate Pairs• Which of the following sets of points

represent functions?

( 1, 4 ); ( 2, 6 ); ( 3, 8 ); ( 4, 10 )

( 1, 3 ); ( 2, 3 ); ( 3, 3 ); ( 4, 3 )

( -1, 8 ); ( -1, 9 ); ( -1, 10 ); ( -1, 11 )

( 1, 1 ); ( 2, 5 ); ( 1, 3 ); ( 4, 6 )

( 0, 4 ); ( -1, 6 ); ( 2, 3 ); ( 0, 4 )

Tables• Which of the following tables represent

functions?

x y x y x y

0 4 1 3 0 4

1 3 2 3 -1 5

2 2 1 3 -2 6

3 1 2 3 -1 7

4 0 1 3 0 8

Scatter Plots

• Which of the following scatter plots represent functions?

Graphs• Which of the following graphs represent

functions?

Domain and Range

Domain = { all reals}Range = { all reals}

Domain = { all reals}Range = { -3 < y < 3 }

Find the domain and range for the function. Write a rule for the function represented by the

graph.

Vertical Line Test

• A test used to see if a graph is a function. If a graph is a function, a vertical line “sweep” will not intersect the graph more than once.

Is this a function?

What is function notation?

• f(x) = x + 2– Pronounced “f of x”– Interchangeable with “y = “

• Why use it?– To restrict the domain

• The domain of f(x) is {3, 4, 5}. Find the range when f(x) = x + 2.

• Range = {5, 6, 7}

Announcements– Quiz corrections: this time gave 50% if missed a few … next time

if any correction is incorrect, you will not receive any points back.– Re-take postponed until Thursday, 10/20

• In order to make an appointment to re-take the test for up to a 90%, you must first show me completed test corrections. Appointments are made either via e-mail or a note

• Unit 1.2 Test grade will be the first test grade of 2nd nine weeks• All students who want to re-take are advised to attend

tutorials this Thursday• All work must be turned in by Wed, 10/12